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Pure carbon nanotubes exhibit '''superlubricity''' - approximately ZERO friction between neighboring tubes in a bundle. In 2013, Zhang et. al. published a paper on [[ https://www.researchgate.net/profile/WZ_Qian/publication/258253770_Superlubricity_in_centimetres-long_double-walled_carbon_nanotubes_under_ambient_conditions/links/0046353390b48ed61f000000.pdf | carbon nanotube superlubricity ]] that measured the intershell sliding force of a 1 centimeter double-wall carbon nanotube (DWCNT). Three diameters were measured, and the tiny pullout force matched theory, pa function of outer tube diameter. ||<-2> Zhang et. al. || ||<-2> Laurent et. al || || Diameter || Pullout || || Inner || Density || Tubes || Pullout || Strength || || nm || Force nN || || nm || Kg/m³ || / m² || Pressure || Kyuri || || 2.73 || 1.37 || || 2.39 || 1951 || 1.16e17 || 159 MPa || 81.5 || || 2.93 || 1.47 || || 2.59 || 1835 || 1.01e17 || 148 MPa || 80.7 || || 3.26 || 1.64 || || 2.92 || 1672 || 8.10e16 || 134 MPa || 80.1 || [[ http://oatao.univ-toulouse.fr/4770/1/Laurent_4770.pdf | Laurent et. al. ]] estimates that the inner tube diameter is 0.34 nM ( $ d_{s-s} $ ) less than the outer tube diameter, and that DWCNT density (g/cm³) is: $ d_{MW} = 6084 { \Large { ( d_{out} ~ - ~ d_{s-s} ) \over { d_{out}^2 } } } $ with $ d_{out} $ and $ d_{s-s} $ in nanometers. I added my own estimations for perfect hexagonally close packed tube density, Tubes/m² $ = \sqrt( 3 ) / 2 D^2 = 0.866 / D^2 $ The pullout pressure $ P = 866 F / D^2 $ mPa if F is nanonewtons and D is nanometers. Results: ||<-2> Zhang et. al. || ||<-2> Laurent et. al || || Diameter || Pullout || || Inner || Density || Tubes || Pullout || Strength || || nm || Force nN || || nm || kg/m³ || / m² || Pressure || Kyuri || || 2.73 || 1.37 || || 2.39 || 1951 || 1.16e17 || 159 MPa || 81.5 || || 2.93 || 1.47 || || 2.59 || 1835 || 1.01e17 || 148 MPa || 80.7 || || 3.26 || 1.64 || || 2.92 || 1672 || 8.10e16 || 134 MPa || 80.1 || These strengths '''for pure, perfect DWCNT''' are less than 0.2% of the minimum strength needed for a space elevator, and 2% of the strength of [[torayca.com/en/download/pdf/torayca_t1100g.pdf | Torayca 1100G carbon fiber]]. Furthermore, given these pullout forces, which will be unevenly distributed in real atomically imperfect materials, the '''stretch will not recover'''; these are not spring forces, but disassembly forces. After the material slides apart, it will not go back together, the hysteresis is unity. This is weak taffy, not a strong elastic material like kevlar or carbon fiber, or even a . The situation is grim but not completely hopeless. In [[ https://doi.org/10.1557/opl.2015.251 | CNT fibers - yarns between the extremes ]], Dr. Thurid Gspann et. al. suggests that defects create load-sharing crosslinks between tubes, but can reduce strength from the theoretical 100 GPa by 30% to 70%. Even with the theoretical "best defect" maximum of 70 GPa, and a density of 1700 kg/m, this '''theoretical''' atomic-precision macro-material will have a strength of 41 Myuri, less than the 48 Myuri (derated by 40% to 34 Myuri) material assumed by the [[ https://www.worldcat.org/oclc/871183396 | 2013 Space Elevators assessment ]]. If ≈ 40 Myuri is potentially possible with '''perfect "precision-defect" CNT''' (based on current pessimistic knowledge), there may be an atomically-perfect 3D material structure with zero hysteresis and 40 Myuri strength. '''''May'' be'''; in 2017, we do not have a scintilla of a clue how to do that. Indeed, these may be self-repairing pseudo-life-like complex nanostructures that can repair and grow themselves under tension, but are far beyond our current understanding and technological imagination. Space elevators have assumed diamond-like crystal tethers since the 1970s, and carbon nanotube tethers since the 1990s. The materials necessary have not yet been discovered, or even imagined in practical detail. |
CNTE
Pure carbon nanotubes exhibit superlubricity - approximately ZERO friction between neighboring tubes in a bundle. In 2013, Zhang et. al. published a paper on carbon nanotube superlubricity that measured the intershell sliding force of a 1 centimeter double-wall carbon nanotube (DWCNT). Three diameters were measured, and the tiny pullout force matched theory, pa function of outer tube diameter.
Zhang et. al. |
|
Laurent et. al |
|||||
Diameter |
Pullout |
|
Inner |
Density |
Tubes |
Pullout |
Strength |
nm |
Force nN |
|
nm |
Kg/m³ |
/ m² |
Pressure |
Kyuri |
2.73 |
1.37 |
|
2.39 |
1951 |
1.16e17 |
159 MPa |
81.5 |
2.93 |
1.47 |
|
2.59 |
1835 |
1.01e17 |
148 MPa |
80.7 |
3.26 |
1.64 |
|
2.92 |
1672 |
8.10e16 |
134 MPa |
80.1 |
Laurent et. al. estimates that the inner tube diameter is 0.34 nM ( d_{s-s} ) less than the outer tube diameter, and that DWCNT density (g/cm³) is:
d_{MW} = 6084 { \Large { ( d_{out} ~ - ~ d_{s-s} ) \over { d_{out}^2 } } } with d_{out} and d_{s-s} in nanometers.
I added my own estimations for perfect hexagonally close packed tube density, Tubes/m² = \sqrt( 3 ) / 2 D^2 = 0.866 / D^2 The pullout pressure P = 866 F / D^2 mPa if F is nanonewtons and D is nanometers. Results:
Zhang et. al. |
|
Laurent et. al |
|||||
Diameter |
Pullout |
|
Inner |
Density |
Tubes |
Pullout |
Strength |
nm |
Force nN |
|
nm |
kg/m³ |
/ m² |
Pressure |
Kyuri |
2.73 |
1.37 |
|
2.39 |
1951 |
1.16e17 |
159 MPa |
81.5 |
2.93 |
1.47 |
|
2.59 |
1835 |
1.01e17 |
148 MPa |
80.7 |
3.26 |
1.64 |
|
2.92 |
1672 |
8.10e16 |
134 MPa |
80.1 |
These strengths for pure, perfect DWCNT are less than 0.2% of the minimum strength needed for a space elevator, and 2% of the strength of Torayca 1100G carbon fiber. Furthermore, given these pullout forces, which will be unevenly distributed in real atomically imperfect materials, the stretch will not recover; these are not spring forces, but disassembly forces. After the material slides apart, it will not go back together, the hysteresis is unity. This is weak taffy, not a strong elastic material like kevlar or carbon fiber, or even a .
The situation is grim but not completely hopeless. In CNT fibers - yarns between the extremes, Dr. Thurid Gspann et. al. suggests that defects create load-sharing crosslinks between tubes, but can reduce strength from the theoretical 100 GPa by 30% to 70%. Even with the theoretical "best defect" maximum of 70 GPa, and a density of 1700 kg/m, this theoretical atomic-precision macro-material will have a strength of 41 Myuri, less than the 48 Myuri (derated by 40% to 34 Myuri) material assumed by the 2013 Space Elevators assessment.
If ≈ 40 Myuri is potentially possible with perfect "precision-defect" CNT (based on current pessimistic knowledge), there may be an atomically-perfect 3D material structure with zero hysteresis and 40 Myuri strength. May be; in 2017, we do not have a scintilla of a clue how to do that. Indeed, these may be self-repairing pseudo-life-like complex nanostructures that can repair and grow themselves under tension, but are far beyond our current understanding and technological imagination.
Space elevators have assumed diamond-like crystal tethers since the 1970s, and carbon nanotube tethers since the 1990s. The materials necessary have not yet been discovered, or even imagined in practical detail.